What is the directrix 3x^2-10x+3 ?

The directrix 3x^2-10x+3 is y=-65/12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix 3x^2-10x+3

directrix

3 x^{2} - 10 x + 3

y = - \frac{65}{12}

Solution steps

Rewrite

y = 3 x^{2} - 10 x + 3

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{16}{3})) = (x - \frac{5}{3})^{2}

(h, k) = (\frac{5}{3}, - \frac{16}{3}), p = \frac{1}{12}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(\frac{5}{3}, - \frac{16}{3})

y-coordinate

y = - \frac{16}{3} - p

y = - \frac{16}{3} - \frac{1}{12}

Refine

y = - \frac{65}{12}

2 y^{2} + 8 x = 0

(x - 2)^{2} = 4 (y + 2)

y = 3 x^{2} - 12 x + 5

(y - 2)^{2} = k (x - 3)

y = - 5 (x - 4)^{2} + 180